SOLUTION: ln(x-1)-ln(x+1)=ln(x+5)

Question 143215: ln(x-1)-ln(x+1)=ln(x+5)
Answer by Edwin McCravy(20056) (Show Source): You can put this solution on YOUR website!




Use this principle of logarithms:  

to rewrite the left side;



Now use the principle that  can be written as 
to rewrite the whole equation:



Do you know how to solve that?  If not post again asking how.
You get

x=-3, x = -2

But these must check in the original problem.



Substitute x=-3 in the original





But there can be no logarithm of a negative number
(except in advanced mathematics, but never in ordinary algebra).

So -3 is NOT a solution

Substitute x=-2 in the original





But, again, there can be no logarithm of a negative number
in ordinary algebra.

Therefore -2 is not a solution either.

Therefore there is no solution to the equation.

Edwin

RELATED QUESTIONS
ln x + ln (x+1)= ln... (answered by stanbon)
ln(x-5)+ln(x+1)=ln40 (answered by Fombitz)
ln(x-5)+ln(x+6)=1 (answered by Alan3354)
ln (x+5) - ln (x-1) = ln... (answered by stanbon)
how do I solve... (answered by stanbon)
ln (5)+ ln(5)= ln (x),... (answered by math_helper)
ln(x+2)-ln(x-1)=1 (answered by lwsshak3)
ln x + ln (x+1-e) =... (answered by stanbon)
ln(x-1)+ln(x+2)=1 (answered by josmiceli)